Solve for $x$ and $y$ using elimination. $\begin{align*}-5x-9y &= 6 \\ -6x-6y &= 3\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-2$ and the bottom equation by $3$ $\begin{align*}10x+18y &= -12\\ -18x-18y &= 9\end{align*}$ Add the top and bottom equations. $-8x = -3$ Divide both sides by $-8$ and reduce as necessary. $x = \dfrac{3}{8}$ Substitute $\dfrac{3}{8}$ for $x$ in the top equation. $-5( \dfrac{3}{8})-9y = 6$ $-\dfrac{15}{8}-9y = 6$ $-9y = \dfrac{63}{8}$ $y = -\dfrac{7}{8}$ The solution is $\enspace x = \dfrac{3}{8}, \enspace y = -\dfrac{7}{8}$.